Geospatial representations of the three dimensional earth are produced in two dimensions, and must be projected into a two dimensional plane. Various projections are suitable, depending on the purpose of the map.
Much of the source material for cartographic applications is made available in the Universal Transverse Mercator (UTM) projection. The U.S. Geological Survey currently supplies Digital Orthographic Photo Quads (DOQ) and Topographic Quads in this projection. However, other cartographic materials are provided in other projections. A common projection format is Geodetic projection.
Geospatial data can be stored in raster format or vector format. In vector format, the cartographic features are typically provided with explicit coordinates. Digital images are typically stored in raster format. Raster or image data is composed of individual pixels with implicit coordinates determined by the projection employed at the creation of the image and any corner coordinates or other georeferencing information.
To transform vector data from one map projection into another map projection type, only the coordinates of the features must be manipulated. To transform raster or image data from one map projection into another map projection type, every pixel is remapped.
A set of equations for transforming UTM data to Geodetic data and Geodetic data to UTM data is provided in J. Snyder, “Map Projections—A Working Manual”, U.S. Geological Survey Professional Paper 1395, United States Government Printing Office, Washington, 1987, also available online at http://onlinepubs.er.usgs.gov/djvu/PP/pp—1395.djvu.
One common method of transforming or “reprojecting” a georeferenced image is with a technique called “rubber sheeting”. In rubber sheeting several control points are chosen from both the source and destination space and a linear transformation matrix defined. This technique works well when the transformation can be accomplished with a set of linear equations. In essence, rubber sheeting allows you to rotate, linearly stretch, and translate the source image. Unfortunately, the transformation from UTM to Geodetic is nonlinear. The result of rubber sheeting on UTM images can be visible discontinuities between adjacent reprojected images as shown in FIG. 1. For example, in the map region 10, the map shows a break between road segments 12 and 14 where adjacent map images meet. Where high levels of accuracy are required, rubber sheeting is not very appropriate for UTM to Geodetic reprojection.
S. Jain and T. Barclay describe a pointwise reprojection method for producing a Geodetic reprojection of an original UTM image in “Adding the EPSG:4328 Geographic Longitude-Latitude Projection to Terra Server”, Technical Report MSR-TR-2003-56, Microsoft Research, Redmond, Wash., 2003. This method uses the Snyder equations and can be more accurate than the rubber sheeting method. Pointwise reprojection operates on each point, or pixel, in the image individually. The color of each pixel in the Geodetic image is determined by converting the pixel's coordinates to UTM, then assigning the color of the corresponding UTM image pixel to the Geodetic image pixel. This pixel by pixel approach becomes processor intensive for large images.